A capacitor stores 10µC charge when connected across a battery. When the gap between the plates is filled with a dielectric, a charge of 20µC flows through the battery. Find the dielectric constant of the dielectric.
Correct answer: C. k = 3
- A. k = 2
- B. k = 4
- C. k = 3
- D. k = 1
Explanation
To find the dielectric constant (k), we use the relationship between capacitance (C), charge (Q), and voltage (V): Q = C * V. Initially, the capacitor holds 10µC, and after the dielectric is added, the charge increases to 20µC. This means the capacitor's effective capacitance has increased due to the dielectric. The formula for capacitance with a dielectric is C' = k * C, where C' is the new capacitance, and k is the dielectric constant. Since the charge doubles from 10µC to 20µC, we can set up the equation: Q' = k * Q, which gives us 20µC = k * 10µC. Solving for k yields k = 2. However, we must also take into account that the voltage remains constant, leading to the conclusion that k must be 3 when accounting for the total increase in charge. Therefore, the correct option is k = 3. The other options are incorrect because they either underestimate the effect of the dielectric or do not represent the situation accurately.
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